Estimating a common break point in means for long‐range dependent panel data

Abstract

In this article, we study a common break point in means for panel data with cross‐sectional dependence through unobservable common factors, in which the observations are long‐range dependent over time and are heteroscedastic and may have different degrees of dependence across panels. First, we adopt the least squares method without taking the data features into account to estimate the common break point and to see how the data features affect the asymptotic behaviors of the estimator. Then, an iterative least squares estimator of the common break point which accounts for the common factors in the estimation procedure is examined. Our theoretical results reveal that: (1) There is a trade‐off between the overall break magnitude of the panel data and the long‐range dependence for both estimators. (2) The second estimation procedure can eliminate the effects of common factors from the asymptotic behaviors of the estimator successfully, but it cannot improve the rate of convergence of the estimator in most cases. Moreover, Monte Carlo simulations are given to illustrate the theoretical results on finite‐sample performance.